Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring

Aleksandra Lj. Erić; Zoran S. Pucanović

doi:doi:10.11648/j.pamj.20130202.11

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Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring

Aleksandra Lj. Erić, Zoran S. Pucanović

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 2)

Received: 2 March 2013 Accepted: Published: 2 April 2013

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Abstract

Let be a commutative ring with identity and its total graph. The subject of this article is the investigation of the properties of the corresponding line graph In particular, we determine the girth and clique number of In addition to that, we find the condition for to be Eulerian.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 2)
DOI	10.11648/j.pamj.20130202.11
Page(s)	51-55
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Total Graph; Line Graph; Commutative Ring

References

[1]	I. Beck, "Coloring of commutative rings", J. Algebra 116, (1988) 208-226.
[2]	D.F.Anderson, P.S. Livingston, "The zero-divisor graph of a commutative ring", J. Algebra 217, (1999), 434-447.
[3]	D.F. Anderson, A. Badawi, "The total graph of a commutative ring", J. Algebra 2008, 320, 2706-2719.
[4]	H.R. Maimani, C. Wickham, S. Yassemi, "Rings whose total graph have genus at most one", Rocky Mountain J. Math., to appear.
[5]	H. Whitney, "Congruent graphs and connectivity of graphs", American Journal of Math. 54 (1932), 150-168.
[6]	Hung-Jen Chiang-Hsieh, Pei-Feng Lee, Hsin-Ju Wang, "The embedding of line graphs associated to the zero-divisor graphs of commutative rings", Israel J. Math. 180, (2010) 193-222.
[7]	Z. Petrović, Z. Pucanović, "The line graph associated to the total graph of a commutative ring", Ars Combinatoria, to appear.
[8]	I. Kaplansky, " Commutative rings", Revised Edition, University of Chicago Press, Chicago, 1974.
[9]	M.F. Atiyah, I.G. Macdonald, "Introduction to commutative algebra", Adison-Wesley Publishing Company, Reading, MA. 1969.
[10]	D.B. West, "Introduction to graph theory", Prantice Hall, Inc., Upper Saddle River, NJ, 1996.
[11]	R. Diestel, "Graph Theory", Third Edition, Graduate Texts in Mathematics 173, Springer-Verlag Berlin Heidelberg, 2005

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APA Style

Aleksandra Lj. Erić, Zoran S. Pucanović. (2013). Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure and Applied Mathematics Journal, 2(2), 51-55. https://doi.org/10.11648/j.pamj.20130202.11

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ACS Style

Aleksandra Lj. Erić; Zoran S. Pucanović. Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure Appl. Math. J. 2013, 2(2), 51-55. doi: 10.11648/j.pamj.20130202.11

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AMA Style

Aleksandra Lj. Erić, Zoran S. Pucanović. Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure Appl Math J. 2013;2(2):51-55. doi: 10.11648/j.pamj.20130202.11

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@article{10.11648/j.pamj.20130202.11,
  author = {Aleksandra Lj. Erić and Zoran S. Pucanović},
  title = {Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {51-55},
  doi = {10.11648/j.pamj.20130202.11},
  url = {https://doi.org/10.11648/j.pamj.20130202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.11},
  abstract = {Let   be a commutative ring with identity and   its total graph. The subject of this article is the investigation of the properties of the corresponding line graph   In particular, we determine the girth and clique number of   In addition to that, we find the condition for   to be Eulerian.},
 year = {2013}
}

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TY  - JOUR
T1  - Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
AU  - Aleksandra Lj. Erić
AU  - Zoran S. Pucanović
Y1  - 2013/04/02
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DO  - 10.11648/j.pamj.20130202.11
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JO  - Pure and Applied Mathematics Journal
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AB  - Let   be a commutative ring with identity and   its total graph. The subject of this article is the investigation of the properties of the corresponding line graph   In particular, we determine the girth and clique number of   In addition to that, we find the condition for   to be Eulerian.
VL  - 2
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Author Information

Aleksandra Lj. Erić
Zoran S. Pucanović

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Plain Text BibTeX RIS

APA Style

Aleksandra Lj. Erić, Zoran S. Pucanović. (2013). Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure and Applied Mathematics Journal, 2(2), 51-55. https://doi.org/10.11648/j.pamj.20130202.11

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ACS Style

Aleksandra Lj. Erić; Zoran S. Pucanović. Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure Appl. Math. J. 2013, 2(2), 51-55. doi: 10.11648/j.pamj.20130202.11

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AMA Style

Aleksandra Lj. Erić, Zoran S. Pucanović. Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring. Pure Appl Math J. 2013;2(2):51-55. doi: 10.11648/j.pamj.20130202.11

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@article{10.11648/j.pamj.20130202.11,
  author = {Aleksandra Lj. Erić and Zoran S. Pucanović},
  title = {Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {51-55},
  doi = {10.11648/j.pamj.20130202.11},
  url = {https://doi.org/10.11648/j.pamj.20130202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.11},
  abstract = {Let   be a commutative ring with identity and   its total graph. The subject of this article is the investigation of the properties of the corresponding line graph   In particular, we determine the girth and clique number of   In addition to that, we find the condition for   to be Eulerian.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
AU  - Aleksandra Lj. Erić
AU  - Zoran S. Pucanović
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130202.11
DO  - 10.11648/j.pamj.20130202.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 51
EP  - 55
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130202.11
AB  - Let   be a commutative ring with identity and   its total graph. The subject of this article is the investigation of the properties of the corresponding line graph   In particular, we determine the girth and clique number of   In addition to that, we find the condition for   to be Eulerian.
VL  - 2
IS  - 2
ER  -

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